Particle in a 1-Dimensional box
claimed by Eathan 4/14/2022 The time-independent Schrodinger Equation is a partial differential equation whose solutions describe the wave function of a quantum system. It is given in the following form. [math]\displaystyle{ -\frac{\hbar^2}{2m}\frac{\partial^2\psi(x)}{\partial x^2} + V(x)\psi(x)= E \psi(x) }[/math]
where
[math]\displaystyle{ \hbar }[/math] is the reduced Planck constant
[math]\displaystyle{ m }[/math] is the mass of the particle
[math]\displaystyle{ \psi(x) }[/math] is the wave function
[math]\displaystyle{ V(x) }[/math] is the potential of the system
[math]\displaystyle{ E }[/math] is the energy of the system
The particle in a 1-Dimensional box is a quantum system in which a particle is bounded in a well with infinite energy at the barrier. Classically, the particle in this system cannot escape. However, in this quantum system, we can demonstrate the particle's quantum tunneling by solving the time-independent Schrodinger Equation.
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The particle in a 1-Dimensional box
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